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Try with weather preset Clear
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Turn Turbulence in Assistance>Piloting to low
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Fly a non-complex stock aircraft like the C152.
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Try without your controllers plugged in (so fly using the keyboard)
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Turn off all 3rd party add-ons except perhaps Input Viewer
Now reintroduce each factor step by step and see if the behaviour returns. Use the Input Viewer mod (.to for it) to see what your contollers are doing.
FWIW it sounds like a controller conflict or calibration issue rather than environmental. But there is no obvious or simple answer, so you will have to troubleshoot it.